Modeling of three-dimensional surfaces using high-level canonical piecewise-linear functions in cylindrical coordinates

In this paper, the potential application of the high-level canonical piecewise-linear model in the field of three-dimensional visualization is proposed. This idea emerges from the premise that a three-dimensional surface can be modeled by a continuous two-dimensional function. In this regard, the main contribution consists in providing a methodology for the construction of such function. For this purpose, the well-known algorithm used in the high-level canonical piecewise-linear model has been modified to achieve functions with greater graphing capability. One of the most notorious changes made with respect to the traditional methodology is the use of a new scheme of function domain partition. Contrary to the simplicial partitioning, in our proposal, an equally distributed angular partitioning is considered. With this, the resulting approximate function is expressed in cylindrical coordinates which overcome the typical limitation of graphs in Cartesian coordinates of only representing single-valued surfaces. Another remarkable change can be found in the range of evaluation of the function. Instead of using an open interval, in our approach, a closed interval from 0 to 2 π is adopted. To support this proposal, illustrative case studies are reported. Numerical simulations demonstrate the effectiveness of this type of representation model not only in visual perception of three-dimensional surfaces, but also in more complex tasks like volume estimation.